Unsteady three-dimensional flowfields are calculated for the Stratospheric Observatory For Infrared Astronomy (SOFIA) at both free-flight cruise and wind tunnel conditions with a view to help in the design process of an acoustically quiet telescope cavity and to understand the flow physics of a three dimensional cavity. The calculation method is based on the numerical solution of thin layer Navier-Stokes equations on a Chimera overset grid system. The Boeing 747-200 aircraft is examined as one option for the SOFIA platform. The flowfield domain is composed of 45 grids consisting of over 4.1 million points. Numerical simulations are performed for both wind tunnel and free-flight cruise conditions at one freestream condition of M(infinity) = 0.85, alpha = 2.5 deg. Comparison of results from wind tunnel simulation show good agreement with experimental data for time-averaged surface pressures, drag for the empennage, and sound pressure levels and power spectra at various locations within the cavity and on the telescope. The presence of the open cavity induces an incremental drag increase, an increased acoustic radiation, and an increase in unsteady pressure loads on the telescope. Its impact on the effectiveness of aircraft control surfaces appears minimal.